Is it permissible for the husband to take back his wife after divorcing her three times, based on her father's request, and is the condition set by the wife's father valid, that the husband says "حلّه لأي رجل آخر" (she is lawful for any other man) when divorcing her?

If a man pronounces a triple divorce, his wife becomes irrevocably divorced from him (baynunah kubra) and is not permissible for him again until after she has married another man. However, if he only agrees to khul‘ (dissolution of marriage initiated by the wife) and does not pronounce a divorce, she becomes revocably divorced from him with one divorce (baynunah sughra), because khul‘ is considered a divorce. In both cases, the wife is free to marry after her waiting period (‘iddah (definition)) ends. It is advisable to refer to the Sharia (definition) courts to resolve the dispute.